We conclude this subsection with a remark on a subtle point concerning the specification
of a definite contraction order among multiple Levi-Civita tensors, in order to reach
an unambiguous canonical form for a projector as well as for the resulting projection in D dimensions.
As discussed in ref. [1]}, the contraction of four Levi-Civita tensors
can lead to different expressions in D dimensions depending on the choice of pairings,
which are not algebraically identical due to the lack of a Schouten identity.
This issue is of no concern for the amplitude of (REF ),
especially if we do the trace over the lepton line using 4-dimensional Dirac algebra
before dealing with the heavy quark line.
Nevertheless, in more general situations to which our projector prescriptions also apply,
one should pair Levi-Civita tensors from inner vertices (of the same fermion line)
in the contraction [1]}, leaving all other Levi-Civita tensors appearing
in the external projectors in a different category that are to be manipulated among themselves.
Once a definite choice of pairing and ordering of Levi-Civita tensors in the contraction
is made, it should be consistently applied in the computations of all terms that contribute to
a (renormalized and subtracted) helicity amplitude.
Alternatively, if several \(\gamma _5\)  matrices from axial non-singlet current vertices
and/or pseudoscalar vertices are present along a fermion line, one can resort to
a fully anti-commuting \(\gamma _5\)  and use the rule \(\gamma _5^2 = 1\)  in \(D\)  dimensions [3]},
in order to bring the power of \(\gamma _5\)  down to 0 or 1 before further manipulations.
This shall lead to the same final result one would get with a thorough implementation of Larin's
prescription of non-singlet axial vector vertices and pseudoscalar vertices [4]}, [1]},
albeit it is computationally more convenient.
